Motion of an Electrified Sphere. 



67 



If P* be the transverse component of the momentum, i. e. the 

 ♦component perpendicular to u in the direction making an acute 

 .angle with w, 



mow* 3sin 2i/r r2n(3 — 2n 2 ) , l-\-n 





16V L 3(1-71*) 



"*iS0 



??ln'^ 



C sin 2^, 



where C is a function of n. 



Expressing the result in a series, we have 



-p _ m w 2 sin 2-yjr Fn 2n d 3n 5 An 7 



.1. 



j 



I have verified thai the values of I > 1 and P 2 given in § 14 

 lead to the above formula for P M by expanding all the quan- 

 tities in (43) in powers of ions far as io 2 , the process involving 

 a good deal of labour. The verification of the formula for 

 P* requires the expansions to be carried as far as ic 3 , and 

 this led to expressions which were so complicated that I 

 abandoned the work. 



Tables V. and VI., which have been prepared for me by 

 my friend and former colleague R. S. Cole, show the values 

 of vP u /m io* and of ©P / /?n io 2 for a few values of n and of yjr. 





Table V. — Values of 





=A-Bj 



sin 2 yjr. 





11. 



A. 



B. 



vPu /)ii 1V 2 . 





if/=0°. 



-,//:= 180°. 



^= 30°.'j/= 45°.' 

 ^=150°. ^=135°. 



i£= 00° J 

 £=120 . 



4/ = 90°. 



01 



00409 



00105 



00409 



00382 



0-0356 



0330 



00304 



02 



00873 



00242 



00873 



00813 



00752 



00692 



00631 



0-3 



01468 



00467 



01468 



01354 



01240 



01125 



01011 



04 



0-2322 



00835 



0-2322 



0-2114 



01905 



0-1696 



01487 



05 



0-3695 



01559 



0-3695 



0-3305 



02915 



0-2525 



02135 



0-6 



0-6204 



0-3099 



06204 



05430 



0-4655 



0-3880 



0-3105 



0-7 



1-1680 



0-6924 



1-1680 



0-9948 



0-8217 



0-6486 



0-4755 



08 



2-7651 



1-9461 



2-7661 



2-2786 



1-7921 



1-3056 



08190 



085 



50427 



38667 1 5-0427 



40760 



3-1094 



21427 



1-1760 



0-9 



11-6575 



! 9-7421 Ll-6675 



9-2220 



6-7865 



4-3510 



1-9154 



F 2 



